U.S. Pat. No. 5,338,196 (which is owned by the Assignee of the present application) teaches, among other things, a second-stage healing abutment for forming and preserving in the mucosa above a dental implant a transmucosal opening large enough to receive an artificial tooth which faithfully replicates a natural tooth being restored. This opening expands in size from the implant to the outer surface of the overlying gingiva, where the opening has width approximating that of the lost natural tooth being replaced, where it emerged from the gums. During the first stage of dental implantation, however, when the implant with its cover screw is left unloaded in the jawbone for a time interval while osseointegration proceeds, the crestal cortical bone tends to grow over the periphery of the cover screw, and this overgrowth must be removed at the beginning of the second stage, if only to permit the cover screw to be removed from the implant. Removing this bone overgrowth is now done by hand. This practice is tedious and imprecise, and potentially harmful to the patient.